Figure REF  shows the \(H/R_\mathrm {p}\)  ratio as a function of planetary mass and irradiation temperature. Contours of constant \(H/R_\mathrm {p}\)  values seem parallel to the boundary between stable and unstable atmospheres. The highest computed values of \(H/R_\mathrm {p}\)  indicate that \(\eta \)  is \(\simeq 0.1\)  for our model, and has no apparent correlation with the CMF or the WMF. This value is almost \(\sim \) 3–4 times higher than the theoretical estimate (\(\eta \)  = 0.026–0.035) found for \(T_\mathrm {irr}\)  = 500–2000 K, \(P_\mathrm {tr}\)  = 10\(^{-3}\) –20 mbar, and \(n_\mathrm {IPM}\)  = 5\(\times \)  10\(^6\)  \(\mathrm {m}^{-3}\)  [1]}. In the currently confirmed population of exoplanetshttp://exoplanet.eu/, assuming pure H2O atmospheres, we find that the \(H/R_\mathrm {p}\)  ratio is mainly in the \(10^{-3}\) –\(10^{-2}\)  range for planets with masses smaller than 2.3 \(M_\) . Using Kepler-51 b's planetary parameters derived by [2]}, we also find that this planet exhibits one of the highest \(H/R_\mathrm {p}\)  ratio (0.013\(^{+0.006}_{-0.010}\) ), which is consistent with the aforementioned \(10^{-3}\) –\(10^{-2}\)  range. Even if the assumption of a pure steam atmosphere is likely to be unrealistic, this computation gives an upper bound to the criterion. This value is most certainly an observational limitation, better detection capabilities will allow to constrain more precisely the boundary between stable and unstable atmospheres based on the \(H/R_\mathrm {p}\)  criterion.
